Symmetric paired points on a parabola

Optional extension

For \(y=\dfrac15(15x-x^2)\):

1. find missing table value \(p\)[2]
2. draw the graph for \(0\le x\le15\)[2]
3. The distinct points \((4,k)\) and \((h,k)\) lie on the curve. Find
   1. \(k\),[2]
   2. \(h\)[2]
4. solve \(\dfrac15(15x-x^2)=0\)[2]
5. state the maximum value.[2]

For graph readings, give values to the nearest 0.1 unit where an exact value cannot be read from the grid. Use the labelled axes and grid provided.